Newform orbit 171.2.v.a

• Label: 171.2.v.a
• Level: $171$
• Weight: $2$
• Character orbit: 171.v
• Analytic conductor: $1.365$
• Analytic rank: $0$
• Dimension: $108$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.v (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.36544187456\)
Analytic rank:	\(0\)
Dimension:	\(108\)
Relative dimension:	\(18\) over \(\Q(\zeta_{9})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 108 q - 3 q^{2} - 12 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} + 3 q^{7} + 12 q^{8} - 24 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
25.1	−0.467288	−	2.65012i	−0.457735	−	1.67047i	−4.92539	+	1.79270i	2.18187	−	1.83080i	−4.21306	+	1.99364i	−1.01242	−	1.75357i	4.36143	+	7.55422i	−2.58096	+	1.52927i	−5.87141	−	4.92670i
25.2	−0.403831	−	2.29024i	−1.71841	+	0.216966i	−3.20274	+	1.16570i	−1.82693	+	1.53297i	1.19085	+	3.84795i	1.29858	+	2.24921i	1.63754	+	2.83630i	2.90585	−	0.745672i	4.24865	+	3.56504i
25.3	−0.378293	−	2.14541i	1.48933	+	0.884255i	−2.58028	+	0.939146i	2.08862	−	1.75256i	1.33369	−	3.52972i	1.71976	+	2.97872i	0.812451	+	1.40721i	1.43618	+	2.63389i	−4.55007	−	3.81796i
25.4	−0.351652	−	1.99432i	−0.903452	+	1.47776i	−1.97425	+	0.718570i	1.25384	−	1.05209i	3.26482	+	1.28211i	−1.67092	−	2.89412i	0.102224	+	0.177058i	−1.36755	−	2.67017i	−2.53912	−	2.13058i
25.5	−0.295630	−	1.67660i	1.28864	−	1.15733i	−0.844205	+	0.307265i	−0.658025	+	0.552148i	−2.32133	−	1.81839i	−0.0396751	−	0.0687193i	−0.937731	−	1.62420i	0.321188	−	2.98276i	1.12026	+	0.940012i
25.6	−0.156900	−	0.889825i	0.444902	+	1.67394i	1.11221	−	0.404813i	−2.93163	+	2.45993i	1.41971	−	0.658526i	1.89997	+	3.29085i	−1.43827	−	2.49116i	−2.60412	+	1.48948i	2.64888	+	2.22268i
25.7	−0.149988	−	0.850625i	−1.33901	−	1.09866i	1.17832	−	0.428873i	−1.72088	+	1.44399i	−0.733709	+	1.30378i	−2.47686	−	4.29004i	−1.40529	−	2.43404i	0.585905	+	2.94223i	1.48640	+	1.24724i
25.8	−0.104796	−	0.594326i	−0.454017	−	1.67149i	1.53714	−	0.559475i	1.32051	−	1.10804i	−0.945828	+	0.444998i	1.70101	+	2.94623i	−1.09709	−	1.90022i	−2.58774	+	1.51777i	−0.796917	−	0.668693i
25.9	−0.0771346	−	0.437452i	−1.51258	+	0.843853i	1.69397	−	0.616555i	0.608387	−	0.510497i	0.485818	+	0.596593i	0.792238	+	1.37220i	−0.844578	−	1.46285i	1.57583	−	2.55280i	−0.270246	−	0.226763i
25.10	−0.0115336	−	0.0654101i	0.607669	+	1.62196i	1.87524	−	0.682531i	1.76671	−	1.48244i	0.0990837	−	0.0584546i	−1.17531	−	2.03569i	−0.132692	−	0.229829i	−2.26148	+	1.97122i	−0.117343	−	0.0984628i
25.11	0.0761154	+	0.431672i	1.73173	−	0.0331392i	1.69884	−	0.618327i	−1.57242	+	1.31942i	0.146117	+	0.745018i	−0.358398	−	0.620764i	0.834553	+	1.44549i	2.99780	−	0.114776i	−0.689242	−	0.578342i
25.12	0.202835	+	1.15033i	0.664179	−	1.59965i	0.597259	−	0.217384i	−0.722472	+	0.606226i	1.97485	+	0.439564i	−0.171559	−	0.297150i	1.53929	+	2.66613i	−2.11773	−	2.12490i	−0.843905	−	0.708120i
25.13	0.240339	+	1.36303i	−1.68464	−	0.402486i	0.0792931	−	0.0288603i	2.47731	−	2.07871i	0.143716	−	2.39295i	−0.827572	−	1.43340i	1.44245	+	2.49840i	2.67601	+	1.35609i	3.42874	+	2.87706i
25.14	0.268294	+	1.52157i	−0.810478	+	1.53073i	−0.363804	+	0.132414i	−2.68532	+	2.25325i	−2.54655	−	0.822514i	−1.60107	−	2.77313i	1.24596	+	2.15806i	−1.68625	−	2.48124i	−4.14892	−	3.48136i
25.15	0.280851	+	1.59278i	−1.25944	−	1.18904i	−0.578700	+	0.210630i	−2.20104	+	1.84689i	1.54017	−	2.33996i	1.67695	+	2.90456i	1.11934	+	1.93875i	0.172379	+	2.99504i	−3.55986	−	2.98707i
25.16	0.384482	+	2.18051i	1.20745	−	1.24180i	−2.72739	+	0.992689i	2.21593	−	1.85939i	3.17199	+	2.15540i	0.311668	+	0.539825i	−0.999053	−	1.73041i	−0.0841321	−	2.99882i	4.90639	+	4.11695i
25.17	0.392563	+	2.22634i	1.22562	+	1.22387i	−2.92308	+	1.06392i	0.336396	−	0.282269i	−2.24362	+	3.20908i	−1.03996	−	1.80126i	−1.25545	−	2.17450i	0.00427843	+	3.00000i	0.760483	+	0.638121i
25.18	0.470315	+	2.66729i	−1.45945	+	0.932748i	−5.01385	+	1.82489i	0.335185	−	0.281253i	−3.17431	−	3.45408i	1.64721	+	2.85306i	−4.51718	−	7.82398i	1.25996	−	2.72259i	0.907827	+	0.761757i
61.1	−2.12061	+	1.77940i	−1.66097	+	0.491103i	0.983415	−	5.57723i	2.93149	+	1.06697i	2.64840	−	3.99697i	0.606857	+	1.05111i	5.07043	+	8.78225i	2.51764	−	1.63141i	−8.11512	+	2.95366i
61.2	−1.91663	+	1.60824i	1.56496	−	0.742234i	0.739724	−	4.19518i	−2.38549	−	0.868249i	−1.80575	+	3.93941i	1.21248	+	2.10008i	2.82711	+	4.89670i	1.89818	−	2.32313i	5.96846	−	2.17234i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
171.v	even	9	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	171.2.v.a	✓	108
3.b	odd	2	1		513.2.z.a		108
9.c	even	3	1		171.2.w.a	yes	108
9.d	odd	6	1		513.2.bd.a		108
19.e	even	9	1		171.2.w.a	yes	108
57.l	odd	18	1		513.2.bd.a		108
171.v	even	9	1	inner	171.2.v.a	✓	108
171.z	odd	18	1		513.2.z.a		108

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
171.2.v.a	✓	108	1.a	even	1	1	trivial
171.2.v.a	✓	108	171.v	even	9	1	inner
171.2.w.a	yes	108	9.c	even	3	1
171.2.w.a	yes	108	19.e	even	9	1
513.2.z.a		108	3.b	odd	2	1
513.2.z.a		108	171.z	odd	18	1
513.2.bd.a		108	9.d	odd	6	1
513.2.bd.a		108	57.l	odd	18	1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(171, [\chi])\).